Abstract
Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ≳ 2m + 3, based on numerical analysis up to N = 13.
Original language | English |
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Pages (from-to) | 1709-1716 |
Number of pages | 8 |
Journal | Journal of Modern Optics |
Volume | 49 |
Issue number | 10 |
DOIs | |
Publication status | Published - 31 Dec 2002 |
Keywords
- computational methods
- numerical methods
- optical data processing
- optical properties
- optical variables measurement
- multiple qubit systems
- quantum computing
- quantum entanglement
- Wootter concurrence formula
- quantum optics